Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions
| dc.contributor.author | Long, Nguyen Thanh | |
| dc.date.accessioned | 2021-07-13T18:38:36Z | |
| dc.date.available | 2021-07-13T18:38:36Z | |
| dc.date.issued | 2005-12-01 | |
| dc.description.abstract | In this paper we consider the nonlinear wave equation problem utt - B(∥u∥²₀, ∥ur∥²₀ (urr + 1/r ur) = ƒ(r, t, u, ur), 0 < r < 1, 0 < t < T, | limr→0+ √rur(r, t)| < ∞, ur(1, t) + hu(1, t) = 0, u(r, 0) = ũ0(r), ut(r, 0) = ũ1(r). To this problem, we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved, in weighted Sobolev using standard compactness arguments. In the latter part, we give sufficient conditions for quadratic convergence to the solution of the original problem, for an autonomous right-hand side independent on u<sub>r</sub> and a coefficient function B of the form B = B(∥u∥²₀) = b₀ + ∥u∥²₀ with b₀ > 0. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Long, N. T. (2005). Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions. Electronic Journal of Differential Equations, 2005(138), pp. 1-18. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13863 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Nonlinear wave equation | |
| dc.subject | Galerkin method | |
| dc.subject | Quadratic convergence | |
| dc.subject | Weighted Sobolev spaces | |
| dc.title | Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions | |
| dc.type | Article |